Effects of the mean free path and relaxation in a model for the aggregation of particles in superfluid media

TL;DR

This study models particle aggregation in superfluid helium, revealing how mean free path and relaxation influence cluster structure, transitioning from compact to fractal forms, aligning with experimental observations.

Contribution

Introduces a two-dimensional aggregation model incorporating relaxation and ballistic moves, elucidating their effects on cluster structure and screening phenomena.

Findings

Relaxation increases average coordination number.

Cluster structure transitions from compact to fractal with size.

Scaling law describes crossover between regimes.

Abstract

In this paper, we study a two-dimensional model for the growth of molecular clusters in superfluid helium at low temperature. In the model, particles of diameter a follow random ballistic moves of length \delta = a-256a. Upon attachment on the cluster surface, particles allow one-step relaxation to the nearest twofold coordinated site. Average coordination numbers of particles show that in the presence of relaxation the screening for incoming particles modifies the microscopic structure of the cluster. These results are in qualitative agreement with experimental aggregation of methane in He droplets, in which large abundance of fully coordinated sites is observed. The average coordination number increases with \delta, showing that screening is relevant when relaxation is present. As the cluster size increases, the corresponding structure clusters changes from a compact to a fractal, typical of ballistic and diffusion limited models, respectively. A scaling ansatz describing the crossover between the two regimes is proposed.